🌿 Surds Simplifier — Pull the Squares Out
🌿 Surds Simplifier — Pull the Squares Out
Four jobs in one desk: strip perfect squares out of a root with every factor shown, collect like surds across an expression, expand (a+b√c)(d+e√c) the FOIL way, and rationalise a denominator by its conjugate — exact fraction arithmetic and worked lines from GCSE to A-level.
Mode
Type √ or sqrt(). An outside number multiplies through: 3√48. A negative inside the root turns imaginary.
Terms joined by + or −, each one of: a plain number, √n, or k√n.
same √c both sides
÷
Pick a mode and go.
Working
Why conjugates work: (a+b√c)(a−b√c) = a² − b²c — the surd cancels and a whole number survives below the line. If that lands on 0, the denominator was zero to begin with and the fraction never existed.